All very confusing this family hitory lark. Don't know about church registers, believe you would have to have appointment sfrom somewhere, unfortunately I have never been able to get there, as following other family trails in the NE and Wales.
I have book of Mon Inscriptions for Everingham, Seaton Ross & Harswell. The only mention of Brightons is the two from WW1 in the church. There are no other family members buried there although there is a George Frederick Brieghton F.R.A. b 1895,died on 21/06/1922 aged 27 ,this is in Everingham church yard.
There is no mention of Pickering family anywhere......
Have also found out that Pocklington, as nearest village which held registers of births,marriages, deaths. There are also Chapmans here in abunance. You may learn more from here thro' Mormon site on BMD'S, who knows.
Will try and find out more........................regards, Colin